How Long?

How long ( how many links ) does my new chain have to be to fit my new 36 tooth cassette, 22/32/44 crank, and XTR long cage rear mech ?? I got one that's 110 links, and it does not appear to be long enough !! Just wanted to ask as I'm new to this stuff.

I don't know. I size by comparison to my old one or by fitting around my largest chainring and largest cog. But, my bikes probably have different chainstays from yours, and if I won't count links for my own stuff...

I prefer the articles on Park Tool for finding answers to this stuff. You'll be sizing it to what's on your bike as in post #2, but without having to watch a video (still with pictures.) In a pinch, retail-packaged chains usually have instructions too.

Put around the 2 biggest ( front and rear ). It has maybe one extra link. Not even sure on that one. It's only 110 links. I think I needs another one lol!! Can I add some links, or is this a big NONO? I think I read something to that effect.

I haven't had to add links in a very long time, but IIRC, you would want to push the last pin (the one that is going to join the additional links to the existing chain) not quite all the way out, then flex it sideways as you are assembling it to the chain until that pin that was not quite all the way out engages the hole.
Sometimes you just need to use a brand new pin, though. See your LBS for that. Reason: Sometimes, when the pin gets pushed back through to join the chain, it damages the side plate of the chain (you might see a little crescent of steel peel out of the side plate) and doesn't hold tight - then the chain works itself apart where you joined it. A good chain tool will prevent this.

-F

PS - If you are not prone to cross-chaining, you can just use your chain at the same length as before. You shouldn't be in 44-36 at any time anyway.